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Hybrid systems can exhibit a range of pathologies that are hard to rule out without making a modeling formalism overly restrictive. Addressing these pathologies, many of which relate to so-called Zeno behaviors, is a prerequisite to being able to give sound definitions of fundamental concepts in hybrid systems, such as reachability.

We propose the use of partial continuous maps (PCM) as trajectories to describe how a hybrid system evolves over time. PCMs enable a notion of trajectory that can go beyond Zeno points.

About Prof. Eugenio Moggi

Professor Eugenio Moggi received his MSc from Pisa (1983) and PhD from Edinburgh (1988). He worked at the University of Cambridge, Edinburgh and Pisa, before moving to Genova in 1990. His most well known research contributions include: cat- egorical semantics of polymorphic types, the study of formal sys- tems for partial functions, notions of computations as monads, metalanguages for computational monads and evaluation logic, categorical semantics of program modules, and type systems and operational semantics for multi-stage programming languages.

From a programming perspective, Alan Turing's epochal 1936 paper on computable functions introduced several new concepts, originated a great many now-common programming techniques, including the invention of what are today known as self-interpreters, using programs as data. The 'blob' model of computation is a recent stored-program computational model, biologically motivated and without pointers or memory addresses. Novelties of the blob model: programs are truly first-class citizens, capable of being automatically executed, compiled or interpreted. The model is Turing complete in a strong sense: a universal interpretation algorithm exists, able to run any program in a natural way and without arcane data encodings. The model appears closer to being physically realisable than earlier computation models. In part this owes to strong finiteness due to early binding; and a strong adjacency property: the active instruction is always adjacent to the piece of data on which it operates.

About Prof. Neil D. Jones

Neil Jones is professor emeritus with the University of Copenhagen, Denmark. Research directions follow two directions: programming languages (compiling, program analysis, partial evaluation, semantics); and the theory of computation and computational complexity. He has published books and a number of articles in both areas. Educated in the U.S. and Canada, Neil Jones has been assistant, associate or full professor at the University of Western Ontario, Pennsylvania State University, University of Kansas, Aarhus University in Denmark, and the University of Copenhagen.